Graphs are a way of representing a rule such as "y is the same as x", "y is equal to x squared" or "x is always equal to 3". Really, it is that simple: the line on a graph represents a rule. At a more advanced level a way of thinking about graphs is that if an equation cannot be solved uniquely the graph is a way of representing the infinity of possible solutions.
Graphs are, in general, a way of representing the infinite number of solutions to an unsolvable equation. Cool!
A graph shows pairs of values: left-and-right and up-and-down represent two different things.
To save time it makes sense to get used to common graphs.
Straight Line Graphs
A graph that is a straight line!
What Different Gradients Look Like (YouTube)
Curved graphs with a predictable pattern depending on the index/power.
Graphs of Odd and Even Powers of Polynomial (YouTube)
More polynomial playlists on the way. Request them if you want them soon!
Other Common Graphs
Some other common types of equation have predicable shapes.
Graph transformations are talked about in other sections of UPmaths. This is section just looks at this topic in a bit more detail.
Transformations of Graphs in Direction of x and y Axes (YouTube)
Order for Combining Transformations in Direction of x and y Axes (YouTube)
It can be good to do quick-fire revision of all the common graph shapes.
Graphs of Functions
A function is a pattern or relationship. Sometimes we do not know the equation or it may not have an equation.
Typical questions about graphs like this involve "transformations".
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